- HAFNIUM DIOXIDE - HfO₂

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints), starting from a rutile-type structure.

Crystal Structure

Because of the translational symmetry all the calculations are performed in the primitive unit cell and not in the conventional unit cell. The following information regarding the structure is given with respect to this primitive unit cell, which sometimes can take an unintuitive shape.

Symmetry (experimental):

Space group:	136		P4_2/mnm
Lattice parameters (Å):	4.5870	4.5870		2.9540
Angles (°):	90.0	90.0		90.0

Symmetry (theoretical):

Space group:	136		P4_2/mnm
Lattice parameters (Å):	4.7736	4.7736		3.1603
Angles (°):	90.0	90.0		90.0

Cell contents:

Number of atoms:	6
Number of atom types:	2
Chemical composition:	0

Atomic positions (theoretical):

Hf:	0.0000	0.0000	0.0000
O:	0.3048	0.3048	0.0000
Hf:	0.5000	0.5000	0.5000
O:	0.1952	0.8048	0.5000
O:	0.6952	0.6952	0.0000
O:	0.8048	0.1952	0.5000

Atom type

We have listed here the reduced coordinates of all the atoms in the primitive unit cell.
It is enough to know only the position of the atoms from the assymetrical unit cell and then use the symmetry to build the whole crystal structure.

Visualization of the crystal structure:

You can define the size of the supercell to be displayed in the jmol panel as integer translations along the three crystallographic axis.
Please note that the structure is represented using the primitive cell, and not the conventional one.

Powder Raman

Powder Raman spectrum

The intensity of the Raman peaks is computed within the density-functional perturbation theory. The intensity depends on the temperature (for now fixed at 300K), frequency of the input laser (for now fixed at 21834 cm^-1, frequency of the phonon mode and the Raman tensor. The Raman tensor represents the derivative of the dielectric tensor during the atomic displacement that corresponds to the phonon vibration. The Raman tensor is related to the polarizability of a specific phonon mode.

Choose the polarization of the lasers.

I ∥

I ⊥

I Total

Horizontal:

Xmin:
Xmax:

Vertical:

Ymin:
Ymax:

Data about the phonon modes

Frequency of the transverse (TO) and longitudinal (LO) phonon modes in the zone-center. The longitudinal modes are computed along the three cartesian directions. You can visualize the atomic displacement pattern corresponding to each phonon by clicking on the appropriate cell in the table below.

1	ac	0	0	0	0
2	ac	0	0	0	0
3	ac	0	0	0	0
4	B1u	111	111	111	111
5	B1g	114	114	114	114	2.096e+37 0.0	1.572e+37 0.0	3.668e+37 0.0
6	Eu	234	234	234	234
7	Eu	234	241	241	234
8	Eu	252	252	252	252
9	Eu	252	347	347	252
10	A2g	386	386	386	386
11	A2u	415	415	415	531
12	B1u	531	531	531	551
13	Eg	551	551	551	551	4.961e+40 26.8	5.271e+40 28.5	1.023e+41 55.3
14	Eg	551	551	551	593	4.961e+40 26.8	8.372e+40 45.2	1.333e+41 72.0
15	Eu	593	593	593	593
16	Eu	593	717	717	717
17	A1g	717	814	814	741	1.307e+41 70.6	5.434e+40 29.4	1.851e+41 100.0
18	B2g	872	872	872	872	1.625e+39 0.9	2.235e+39 1.2	3.860e+39 2.1

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥